The problem is this. I've lived under a single payer system and been in a situation similar to yours. My grandmother fell and injured her back. It took a year and a half for her to get treatment because of the wait list. She died, shortly after her name came up.
Single payer sounds great but doesn't work. The answer is lower taxes so that people like you can save to protect your families. Obamacare is unaffordable for most people.
What country did you live in?
I've noticed that most of the stereotypical single payer problems (wait times, resource shortages) tend to happen in countries that are single
provider in addition to being single payer. (Like the UK and other countries where all hospitals and clinics are government-owned and all healthcare workers are government employees.)